Let f:R- 3 5 R be defined by f(x)= 3x+2 5x-3 . Then, - Vidyadip

MCQ

Let $\text{f}:\text{R}-\Big\{\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be defined by $\text{f(x)}=\frac{3\text{x}+2}{5\text{x}-3}.$ Then,

✓
$f^{-1}(x)=f(x)$
B
$f^{-1}(x)=-f(x)$
C
$f \circ f(x)=-x$
D
$\text{f}^{-1}(\text{x})=\frac{1}{19}\text{f(x)}$

✓

Answer

Correct option: A.

$f^{-1}(x)=f(x)$

Given function is $\text{f}:\text{R}-\Big\{\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be defined by $\text{f(x)}=\frac{3\text{x}+2}{5\text{x}-3}$
fo $f(x) = f(f(x))$
$=\text{f}\Big(\frac{3\text{x}+2}{5\text{x}-3}\Big)$
$=\frac{3\big(\frac{3\text{x}+2}{5\text{x}-3}\big)+2}{5\big(\frac{3\text{x}+2}{5\text{x}-3}\big)-3}$
After solving you will get
$f(f(x)) = x$
Also, $f^{-1}(x) = f(x)$ you can check.

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